Hi
The Oxford Dictionary of National Biography has an entry for Henry which starts
'Lambert, Henry (d. 1813), naval officer, younger son of Captain Robert Lambert (d. 1810), '
Wikipedia says of Henry
'During his career, Lambert served in numerous ships and several military actions with success, participating in the capture of Île Bonaparte in the Indian Ocean as second in command under Josias Rowley.'
Sir Josias Rowley 1765-1842 naval officer. His uncle Sir Joshua Rowley 1734-1790 was also a naval officer.
On the otherhand John Lambert's entry in ODof NB begins
'Lambert, Sir John (1772–1847), army officer, was born on 28 April 1772, the son of Captain Robert Alexander Lambert RN (c.1732–1801), '
Possible baptisms
ROBERT LAMBERT
Christening: 08 MAY 1771 Old Alresford, Hampshire
Father: ROBERT LAMBERT
Mother: CATHARINE
JOHN LAMBERT
Christening: 23 MAY 1772 Old Alresford, Hampshire
Father: ROBERT LAMBERT
Mother: CATHARINE
THOMAS ROWLEY LAMBERT
Christening: 20 AUG 1776 Old Alresford, Hampshire
Father: ROBERT LAMBERT
Mother: CATHARINE
Marriage
19th January 1768 Kilmeston Hampshire
Robert Lambert
Catherine Byndloss
Kilmeston and Old Alresford are just over 5 miles apart.
Regards
Valda